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This note concerns the paper "On the controllability of a coupled system of two Korteweg-de Vries equations" by Micu et al. [2]. They study a nonlinear coupled system of two Korteweg-de Vries equations and prove that the system is controllable by using four boundary controls. Here, we prove that in some cases it is possible to get the controllablity of the system by using only two controls. This can be done depending on both the spatial domain and the control time. [ABSTRACT FROM AUTHOR]

We point out that the analysis of Piotrowski and Sladkowski of the paradox described by Astumian has a flaw since they consider a different game. [ABSTRACT FROM AUTHOR]

In this paper, the newly-developed condensed Galerkin element of polynomial degree m ̄ for first-order initial-value problems is reformulated for and extended to the structural dynamic equations, yielding a high-performance dynamic element of one-step, unconditionally stable type with the conventional finite element (FE) convergence O (h m ̄ + 1) within the element and the extra-superconvergence O (h 2 m ̄ + 2) at the element end-nodes. Further, based on the element energy projection (EEP) technique, a superconvergence EEP formula for the condensed element is proposed in the paper and mathematical analysis is presented to prove that the derived EEP solution gains a superconvergence O (h m ̄ + 2) , which is an order higher than the FE solution of O (h m ̄ + 1) for all element degree m ̄ ≥ 1 and is hence qualified to serve as a point-wise error estimator. As a result, a simple, efficient, and reliable algorithm with adaptive time-stepping controlled by the maximum norm is proposed. Representative numerical examples are presented to verify the validity of the proposed theorems and to demonstrate the high performance of the proposed element and the associated adaptivity algorithm. [ABSTRACT FROM AUTHOR]

At present, the informatization of basic education quality assessment has become a hot topic in the field of education and is playing an increasingly important role. Based on the theory of deep convolutional neural network, this paper adopts the methods of mathematical analysis and experimental research to construct a regional basic education quality assessment model. The model solves the data informatization problem of education quality assessment. In the simulation process, two key modules of data self-assessment and expert assessment of the deep convolutional neural network are realized by ASENET+SQL SERVER, and the assessment results are integrated by using the weighted average method and the fuzzy comprehensive assessment method. The experimental results show that the quantitative analysis of the quality assessment is carried out by using the logic and support relationship, and the results of comprehensive qualitative analysis and quantitative analysis are realized and segmented when the threshold level is 9, the MIOU obtains the highest value of 0.7501, and the MIOU of the multi-stage method of the quality evaluation model proposed in this paper is 0.8116, which is 6.15% points higher than the traditional multi-stage algorithm, which effectively improves the current stage area quality of basic education. [ABSTRACT FROM AUTHOR]

The increasing demand for low voltage, power efficient, high-speed analog-to-digital converters (ADCs) results in the improvement of speed and power of regenerative dynamic comparator. In this paper, a dual-tail dynamic comparator is used with two extra transistors in the latch stage. These extra transistors help in the increase of transconductance of the latch stage, which helps decrease the delay of the proposed comparator. Mathematical analysis is done for the proposed architecture; this gives the idea of reducing the delay of the comparator with an increase in the transconductance of the comparator. The simulation and layout of the proposed comparator are done on the Cadence software with 90 nm CMOS technology. This proposed design is simulated with a 2 GHz clock frequency at supply voltage of 1 V. The proposed architecture consumes a power of 39.19 μ W and a delay of 143.12 ps at 1 V supply voltage, 5 mV input difference voltage and 0.9 V common mode voltage. The Monte Carlo simulation of the proposed architecture for power, delay, power delay product (PDP) and offset is also demonstrated in this paper. Process corner analysis is done for power, delay and PDP. [ABSTRACT FROM AUTHOR]

This paper describes a theoretical framework and computational methods of a thin layer coating of a non-Newtonian polymeric material while it moves through a tiny space among two inverted rollers. Order of magnitude is accustomed to clarify the nondimensional forms of the governing equations. Semi-analytical solutions of pressure gradient, velocity profile and rate of the flow are acquired via optimal homotopy asymptotic method (OHAM). The graphical representation depicts the physical quantities of the effects of velocity profile ratio k and Weissenberg number We. It is observed that by increasing the values of k and We, velocity profile decreases while pressure distribution increases. [ABSTRACT FROM AUTHOR]

The security of mobile wireless sensor networks has captivated extensive attention of researchers because of their wide range of applications and vulnerability to attacks caused by malware. In this paper, we investigate a delayed malware propagation model on mobile wireless sensor network incorporating nonlinear incidence rate, logistic growth rate and recovery rate. Local asymptotic stability of the endemic equilibrium and existence of Hopf bifurcation at crucial value of the time delay are analyzed. Then, properties of Hopf bifurcation are explored. Specifically, global exponential stability is investigated via linear matrix inequality. An example is presented finally to underline the effectiveness of findings in our paper numerically and graphically. [ABSTRACT FROM AUTHOR]

When people interact, their behavior tends to become synchronized, a mutual coordination process that fosters short-term adaptations, like increased affiliation, and long-term adaptations, like increased bonding. This paper addresses for the first time how such short-term and long-term adaptivity induced by synchronization can be modeled computationally by a second-order multi-adaptive neural agent model. It addresses movement, affect and verbal modalities and both intrapersonal synchrony and interpersonal synchrony. The behavior of the introduced neural agent model was evaluated in a simulation paradigm with different stimuli and communication-enabling conditions. Moreover, in this paper, mathematical analysis is also addressed for adaptive network models and their positioning within the landscape of adaptive dynamical systems. The first type of analysis addressed shows that any smooth adaptive dynamical system has a canonical representation by a self-modeling network. This implies theoretically that the self-modeling network format is widely applicable, which also has been found in many practical applications using this approach. Furthermore, stationary point and equilibrium analysis was addressed and applied to the introduced self-modeling network model. It was used to obtain verification of the model providing evidence that the implemented model is correct with respect to its design specifications. [ABSTRACT FROM AUTHOR]

The sterile insect technique (SIT) has been applied as an alternative method to reduce or eradicate mosquito-borne diseases. To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations, in this paper, we further extend the work in [J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11(S2) (2017) 316–333] and formulate delayed models for interactive wild and sterile mosquitoes, which can depict wild mosquito population undergoing distinct stages of development during a lifetime. By performing mathematical analysis, the threshold dynamics of the proposed models are explored, respectively. In particular, Hopf bifurcation phenomena are observed as the delay τ is varying. Numerical examples illustrate our findings. [ABSTRACT FROM AUTHOR]

Currently, diabetic retinopathy is still screened as a three-stage classification, which is a tedious strategy and along these lines of this paper focuses on developing an improved methodology. In this methodology, we taught a convolutional neural network form on a major dataset, which includes around 45 depictions to do mathematical analysis and characterization. In this paper, DR is constructed, which takes the enter parameters as the HRF fundus photo of the eye. Three classes of patients are considered — healthy patients, diabetic's retinopathy patients and glaucoma patients. An informed convolutional neural system without a fully connected model will also separate the highlights of the fundus pixel with the help of the enactment abilities like ReLu and softmax and arrangement. The yield obtained from the convolutional neural network (CNN) model and patient data achieves an institutionalized 97% accuracy. Therefore, the resulting methodology is having a great potential benefiting ophthalmic specialists in clinical medicine in terms of diagnosing earlier the symptoms of DR and mitigating its effects. [ABSTRACT FROM AUTHOR]

Linear complementarity problems are fundamental in various mathematical fields, and it is widely recognized that these problems have a unique solution if and only if the matrix related to them is a P-matrix. However, determining whether a matrix is a P-matrix can be extremely challenging or even impossible, especially for large matrices. In this paper, we present a method for establishing the existence and uniqueness of the solution to linear complementarity problems without the need for P-matrix verification. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to model the effects of misidentification in the transmission dynamics of the super yeast, Candida auris (or C. auris), among patients receiving treatment in the Intensive Care Units (ICUs). The mathematical analysis is carried out by obtaining the reproduction number of the C. auris model using the next generation matrix and utilizing it as a threshold value to establish the local and global stability properties at the points of equilibria. The numerical investigations carried out in this paper establish the outcomes of the effect of variations in the values of important parameters on the dynamics of C. auris colonization and infections in the health care settings. The corresponding results from the numerical simulations are illustrated graphically. [ABSTRACT FROM AUTHOR]

A nonclassical model known as the guava model with the conformable derivative describing the interaction of guava pests and natural enemies is studied in this paper. To this end, first the Adams–Bashforth–Moulton predictor–corrector (ABM-PC) scheme is adopted to numerically solve the guava model with the conformable derivative such that its performance is examined using the finite-difference (FD) method. The truncation error of the ABM-PC scheme is then presented in a detailed way. The effect of the order of the conformable derivative on the dynamical characteristics of guava pests and natural enemies is investigated by considering a series of graphical representations. In the end, based on the results given in this study, it is shown which day is more beneficial to harvest the guava. [ABSTRACT FROM AUTHOR]

In this paper, we study an age-structured population model with non-local diffusion and distributed delay. By using the non-densely defined operators and extended phase spaces, we first rewrite the model into an abstract ordinary differential equation. Then we prove the existence of the solution of the model by using the operator semigroup theory. Finally, we study the spectrum of the non-densely defined operators and analyze the asymptotic behavior via asynchronous exponential growth. Our results extend the results for the age-structured population models without time delay. [ABSTRACT FROM AUTHOR]

In this paper, we use a previously developed measles model to forecast measles in Turkey for the period 1970–2021. We study the structural identifiability of the model both by hand and using software. By hand, we assume the prevalence and the total population size are given. Using software, we assume the incidence and the total population size are given. The model is structurally identifiable if one of the three parameters is fixed. We notice that Turkey has a significant change in time of the immigration rate and vaccination proportions, so we assume these two quantities are time-dependent. We fit the nonautonomous model to the measles incidences in Turkey for 1970–2021. We perform practical identifiability of the fitted model, and find that all parameters but one are practically identifiable. When fixing the unidentifiable parameter to a value derived from additional data, we obtain that all parameters are practically identifiable. [ABSTRACT FROM AUTHOR]

In this paper, we establish the validity of the so-called Bounded Approximation Property (BAP) for a comprehensive class of translation and modulation invariant Banach spaces (B, ∥ · ∥B) of tempered distributions on the Euclidean space ℝ d . In fact, such spaces have a double module structure, over some Beurling algebra with respect to convolution, and with respect to pointwise multiplication over some Fourier Beurling algebra. Combining this double module structure with functional analytic arguments which describe the approximation of convolution operators by discrete convolutions we are able to verify the BAP, in fact, for most cases even the Metric Approximation Property (MAP) for such Banach space. The family of spaces under consideration is very rich and contains virtually all the classical function spaces relevant for mathematical analysis, as long as the Schwartz space (ℝ d) is dense in (B, ∥ · ∥B). In particular, all the reflexive spaces in this family are included. Moreover, this family of Banach spaces is closed with respect to intersections, sums and various interpolation methods. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the classical SIR epidemic model by replacing the simple bilinear transmission rate by a nonlinear one. Our results show that in the presence of environmental fluctuations represented by Brownian motion and that mainly act on the transmission rate, the generalized non-concave force of infection adopted here, greatly affects the long-time behavior of the epidemic. Employing the Markov semigroup theory, we prove that the model solutions do not admit a unique stationary distribution but converge to 0 in p th moment for any p > 0. Furthermore, we prove that the disease extinguishes asymptotically exponentially with probability 1 without any restriction on the model parameters and we also determine the rate of convergence. This is an unexpected qualitative behavior in comparison with the existing literature where the studied epidemic models have a threshold dynamics behavior. It is also a very surprising behavior regarding the deterministic counterpart that can exhibit a rich qualitative dynamical behaviors such as backward bifurcation and Hopf bifurcation. On the other hand, we show by several numerical simulations that as the intensity of environmental noises becomes sufficiently small, the epidemic tends to persist for a very long time before dying out from the host population. To solve this problem and to be able to manage the pre-extinction period, we construct a new process in terms of the number of infected and recovered individuals which admits a unique invariant stationary distribution. Finally, we discuss the obtained analytical results through a series of numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is the first one in a series of papers where we lay special attention on syntax and semantics in knowledge base theory. The main goal of the present paper is to set up all necessary mathematical background for the definition of a knowledge-base model which will be introduced in the next paper. We should emphasize that in these papers we develop a slightly different approach to the knowledge-base model than in the previous ones. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented for the mathematical modeling and analysis of the DC–DC Buck Converter output voltage. This paper consists of the demonstration of a mathematical model for the converter transient response submitted to a pulse width modulated (PWM) input voltage, resulting in accurate symbolic expressions for the output voltage. The novelty of the method is the capability of the expressions derived to describe correctly the behavior of the converter submitted to time-varying control reference input signals modulating the switch pulse width. The mathematical model was then validated by comparing it with the responses obtained using the Runge–Kutta numerical method. By using different circuit parameters and PWM input signals with constant and time-varying duty cycles, it was possible to validate the model for different cases, showing the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Reduced population growth at low density has important implications for conservation, colonization success, and wildlife management. In this context, the Allee effect, i.e. the positive relationship between per capita growth rate and biomass of small population density, is a crucial biological phenomenon since it is directly related to population extinction. The present paper deals with a two-species interacting model with a predator–prey relationship, where the prey population experiences the mate-finding Allee effect caused by the predator. We assume that the searching efficiency of prey individuals decreases linearly with predator density due to predation fear and investigate how predation intensity affects predator–prey dynamics. Moreover, we consider the Monod–Haldane type functional response for predator–prey interactions, which shows group defense of prey against the predator. We provide detailed mathematical analyses, including the positivity and boundedness of solutions, all biologically feasible equilibria, and their local and global stabilities. From our detailed mathematical analyses, we observe that when the carrying capacity of prey is low, at most one interior equilibrium exists, and system dynamics is simple compared to the case with high carrying capacity in which multiple coexistence equilibria may exist. We discuss three codimension-one bifurcations mathematically, e.g. Hopf bifurcation, transcritical bifurcation, saddle-node bifurcation. We notice bistability in the system when there are two interior equilibria with high carrying capacity. However, a unique attractor exists when there is only a single interior equilibrium and both populations persist. We perform extensive numerical simulations by varying two parameters simultaneously and explore how the system dynamics become complex when carrying capacity is high compared to low carrying capacity. Moreover, we discuss other important biological phenomena, e.g. the paradox of enrichment, bubbling phenomenon, etc. [ABSTRACT FROM AUTHOR]

Quantitative phase imaging (QPI) technology is one of the important techniques for nondestructive imaging of a cell's morphology. In QPI, the decoupling of refractive index (RI) and thickness of a cell is a key problem. We aim at the multiple hypothesis constraints (MHC) shortcomings of the traditional method in the decoupling of multi-media and nonspherical cells. A method is proposed to decouple the RI and the thickness of a cell under three-wavelength phase imaging in this paper. In this method, the sample's RI and thickness distributions can be obtained by solving three-wavelength phase equations using the approximate setting under dispersion based on the optical dispersion theories. In simulation experiments, the results show that the method can effectively decouple the RI and thickness for homogeneous and multi-media nonspherical cells and has high accuracy. Because the method in this paper is obtained by using few approximate assumptions and strict mathematical analysis, it can decouple the RI and thickness of nuclear cells with any shape, and moreover, it provides an important basis for the technological development of cell morphology analysis. [ABSTRACT FROM AUTHOR]

This paper studies cobordism and concordance for virtual knots. We define the affine index polynomial, prove that it is a concordance invariant for knots and links (explaining when it is defined for links), show that it is also invariant under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. Information on determinations of the four-ball genus of some virtual knots is obtained by via the affine index polynomial in conjunction with results on the genus of positive virtual knots using joint work with Dye and Kaestner. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case 0 < β ≤ 1 , where β is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when β > 1. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm. [ABSTRACT FROM AUTHOR]

The growing demand for maintaining secure communication channels with the advancements in digital technologies has led to an intensified interest in designing reliable image encryption schemes. Despite various encryption schemes that have been used, some are considered to have insecurity regarding data transmission and multimedia. Motivated by this concern, this paper proposes a new color image encryption algorithm of a multi-key generation-based nD-Hyperchaotic (HC) system. The new algorithm achieves Shannon’s confusion and diffusion principles using a two S-box generation approach, where the first S-box is generated from the proposed nD-HC system and the resulting sequence is used to increase encryption complexity, while the second S-box is generated from (n + i)D-HC system. Afterward, mathematical analysis is carried out to showcase the robustness and efficiency of the proposed algorithm, as well as its resistance to visual, statistical, differential, and brute-force attacks. The proposed scheme successfully passes all NIST SP 800 suite tests. The cryptographic system demonstrated by the proposed scheme has proven to have outstanding performance through simulation tests, which indicates promising potential applicability aspects in secure and real-time image communication settings. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a mathematically reasonable and simplest population dynamics model based on Mark Granovetter’s idea for the spread of a matter (rumor, innovation, psychological state, etc.) in a population. The model is described by a one-dimensional difference equation. Individual threshold values with respect to the decision-making on the acceptance of a spreading matter are distributed throughout the population ranging from low (easily accepts it) to high (hardly accepts). Mathematical analysis on our model with some general threshold distributions (uniform; monotonically decreasing/increasing; unimodal) shows that a critical value necessarily exists for the initial frequency of acceptors. Only when the initial frequency of acceptors is beyond the critical, the matter eventually spreads over the population. Further, we give the mathematical results on how the equilibrium acceptor frequency depends on the nature of threshold distribution. [ABSTRACT FROM AUTHOR]

This paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important research perspectives related to new, emerging trends. The presentation addresses the scaling problem corresponding to microscopic (individual-based), mesoscopic (kinetic), and macroscopic (hydrodynamic) modeling and analysis. A multiscale vision guides the overall content of the paper. The critical analysis of the overall content naturally leads to research perspectives. A selection of them is brought to the attention of the interested reader together with hints on how to deal with them. [ABSTRACT FROM AUTHOR]

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation. [ABSTRACT FROM AUTHOR]

In the light of the analogy between electromagnetism and fluid dynamics, the Maxwell-type equations of compressible fluids are reformulated on the basis of spacetime algebra. In this paper, it is proved that this algebra provides an efficient mathematical tool for describing fluid fields in a compact and elegant way. Moreover, the fluid wave equation in terms of potentials are derived in a form similar to electromagnetic and gravitational counterparts previously derived using spacetime algebra. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]

Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution's existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange's interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes. [ABSTRACT FROM AUTHOR]

This paper represents a new integrable trans-admittance mode universal filter employing an active building block, i.e., Voltage Differencing Current Conveyor, and all grounded passive elements. The proposed circuit can easily realize all five, widely used, filter responses, i.e., bandpass, high pass, low pass, all pass and band-reject. The designed circuit configuration provides favorable impedances at the input as well as output ports. Independent tunability of its gain parameter and orthogonal tunability of its quality factor and operating frequency are some of the noteworthy features of the designed circuit. The simulations of the designed filter are verified by 180-nm Complementary Metal Oxide Semiconductor (CMOS) technology in the SPICE simulation environment. Validation of the proposed design is done by experimental work along with the regular mathematical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we present a brief history of artificial intelligence (AI) research for more than 70 years since its inception. We begin with an analysis of the mathematical, engineering, psychological and philosophical foundations enabling modern AI. We then outline and give examples of the three primary research thrusts the discipline has taken over its existence. We conclude offering both important criticisms as well as describing the future promise for current AI research and practice. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behavior of the modified May–Holling–Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. Detailed mathematical analysis and numerical evaluations, including the situation of ecosystem collapsing, have been presented to discuss the coexistence of species', stability, occurrence of different bifurcations (saddle-node, transcritical, and Hopf) in three cases in the presence of prey and alternative resources, in the absence of prey and in the absence of alternative resources. It has been obtained that the multiple coexisting states and their stability are outcomes of variations in predation rate for alternative resources. Also, the occurrence of Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation are due to variations in the parameters of dynamic alternative resources. The impact of dynamic alternative resources on species' density reveals the fact that if the predation rate for alternative resources increases, then the prey biomass increases (under some restrictions), and variations in the predator's biomass widely depend upon the quality of food items. This study also points out that the survival of predators is possible in the absence of prey. In the theme of ecological balance, this study suggests some theoretical points of view for the eco-managers. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model of Hepatitis C Virus (HCV) infection. We present a compartmental mathematical model involving healthy hepatocytes, infected hepatocytes, non-activated dendritic cells, activated dendritic cells and cytotoxic T lymphocytes. The derivative used is of non-local fractional order and with non-singular kernel. The existence and uniqueness of the system is proven and its stability is analyzed. Then, by applying the Laplace Adomian decomposition method for the fractional derivative, we present the semi-analytical solution of the model. Finally, some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions. [ABSTRACT FROM AUTHOR]

It is known that the integral cohomology algebra of any smooth compact toric variety XΣ associated to a complete regular fan Σ is isomorphic to the Stanley-Reisner algebra ℤ[Σ] modulo the ideal JΣ generated by linear relations determined by Σ. The aim of this paper is to show how to determine the integral cohomology algebra of a toric variety (in particular, a projective toric variety) associated to a certain simplicial fan. As a consequence, we confirm our expectation that for a certain simplicial fan the integral cohomology algebra is also given by the same formula as in a complete regular fan. [ABSTRACT FROM AUTHOR]

The RL and RC circuits are analyzed in this research paper. The classical model of these circuits is generalized using the modern concept of fractional derivative with Mittag-Leffler function in its kernel. The fractional differential equations are solved for exact solutions using the Laplace transform technique and the inverse transformation. The obtained solutions are plotted and presented in tables to show the effect of resistance, inductance and fractional parameter on current and voltage. Furthermore, the statistical analysis is presented to predict the seasonal of time and other parameters on the current flowing in the circuit. The statistical analysis shows that the variation in current is insignificant with respect to time and is more significant with respect to other parameters. [ABSTRACT FROM AUTHOR]

This paper introduces a Multi-Agent based Optimization Method for Combinatorial Optimization Problems named MAOM-COP. In this method, a set of agents are cooperatively interacting to select the appropriate operators of metaheuristics using learning techniques. MAOM-COP is a flexible architecture, whose objective is to produce more generally applicable search methodologies. In this paper, the MAOM-COP explores genetic algorithm and local search metaheuristics. Using these metaheuristics, the decision-maker agent, the intensification agents and the diversification agents are seeking to improve the search. The diversification agents can be divided into the perturbation agent and the crossover agents. The decision-maker agent decides dynamically which agent to activate between intensification agents and crossover agents within reinforcement learning. If the intensification agents are activated, they apply local search algorithms. During their searches, they can exchange information, as they can trigger the perturbation agent. If the crossover agents are activated, they perform recombination operations. We applied the MAOM-COP to the following problems: quadratic assignment, graph coloring, winner determination and multidimensional knapsack. MAOMCOP shows competitive performances compared with the approaches of the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on two very important questions: "what is the future of a hybrid mathematical structure of soft set in science and social science?" and "why should we take care to use hybrid structures of soft set?". At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence. [ABSTRACT FROM AUTHOR]

Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number ℜ 0 is defined. The global stability of steady states is determined by rigorous mathematical analysis. When ℜ 0 < 1 , the disease-free equilibrium E 0 is globally asymptotically stable. When ℜ 0 > 1 , the system has a unique positive periodic solution E * , and E * is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number ℜ 0 is solved by the Sobol global sensitivity analysis method, and the results show that the effects of the parameters β 0 and α on ℜ 0 are remarkable. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a new Ito stochastic differential equation model for untreated human glioblastomas. The model was the best fit of the average growth and variance of 94 pairs of a data set. We show the existence and uniqueness of solutions in the positive spatial domain. When the model is restricted in the finite domain (0 , b) , we show that the boundary point 0 is unattainable while the point b is reflecting attainable. We prove there is a unique ergodic stationary distribution for any non-zero noise intensity, and obtain the explicit probability density function for the stationary distribution. By using Brownian bridge, we give a representation of the probability density function of the first passage time when the diffusion process defined by a solution passes the point b firstly. We carry out numerical studies to illustrate our analysis. Our mathematical and numerical analysis confirms the soundness of our randomization of the deterministic model in that the stochastic model will set down to the deterministic model when the noise intensity approaches zero. We also give physical interpretation of our stochastic model and analysis. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo type of fractional derivative, this research paper is the analysis of a mathematical model of generalized thermoelastic diffusion with memory-dependent derivative (MDD) for an isotropic infinite medium with a cylindrical cavity in the context of dual-phase lag model. The surface of the cavity is traction free and subjected to harmonically heat sources with constant angular frequency of thermal vibration. Laplace transform technique has been used to solve the problem. Later eigenvalue approach is used to obtain the analytical expressions for different physical fields in the transformed domain. Finally to obtain the solutions in the real-time domain, the Riemann-sum approximation method is used. According to the graphical representations corresponding to the numerical results, the effect of heat source speed on temperature, displacement, stress, mass concentration and chemical potential are studied. The effect of memory-dependent parameters, as well as in the absence of MDD on physical quantities are also demonstrated. [ABSTRACT FROM AUTHOR]

The existence of compact simply-connected K-contact, but not Sasakian, manifolds has been unknown only for dimension 5. The aim of this paper is to show that the Kollár's simply-connected example which is a Seifert bundle over the complex projective space ℂℙ2 and does not carry any Sasakian structure is actually a K-contact manifold. As a consequence, we affirmatively answer the above existence problem in dimension 5, establishing that there are infinitely many compact simply-connected K-contact manifolds of dimension 5 which do not carry a Sasakian structure. [ABSTRACT FROM AUTHOR]

This paper is devoted to the modeling, qualitative analysis and simulation of Darwinian selection phenomena and their evolution. The approach takes advantage of the mathematical tools of the kinetic theory of active particles which are applied to describe the selective dynamics of evolution processes. The first part of the paper focuses on a mathematical theory that has been developed to describe mutations and selection processes. The second part deals with different modeling strategies and looks ahead to research perspectives. [ABSTRACT FROM AUTHOR]

No abstract received. [ABSTRACT FROM AUTHOR]

No abstract received. [ABSTRACT FROM AUTHOR]

This paper proposes new cointegration tests based on instrumental variable (IV) estimation. An important property of our tests is that the asymptotic distribution remains standard normal (orChi-square) regardless of the number of regressors, differing deterministic terms, structural dummies, and inclusion of stationary covariates. Thus, our IV cointegration tests have the operational advantage that they do not depend on nuisance parameters. As such, we can incorporate stationary covariates into a model to enhance power without affecting the asymptotic distribution of the test. This is important because it alleviates the need to tabulate the critical values for every possible case or to bootstrap the critical values. [ABSTRACT FROM AUTHOR]

In our previous paper, we studied the braid index of the Kanenobu knot k(n) for n ≥ 0. In this paper, we study the braid index of the Kanenobu knot K(a, b) for a, b ∈ ℤ. In particular, k(n) is K(2n, -2n). The MFW inequality is known for giving a lower bound of the braid index of an oriented link by applying the HOMFLYPT polynomial. The HOMFLYPT polynomial of K(a, b) is given by Professor Taizo Kanenobu. Therefore, we have a lower bound of the braid index of K(a, b). The purpose of this paper is to give an upper bound of the braid index of K(a, b). As a result, we determine the braid indices of infinitely many Kanenobu knots. [ABSTRACT FROM AUTHOR]

In many decision-making problems, different methods usually yield different results. In this paper, we study all possible rankings of alternatives produced by applying a set of aggregation functions on a decision matrix. Those possible rankings depend on the aggregation functions that we use and the structures of the decision matrix. The aim of this paper is to investigate structures and properties of decision matrices and aggregation function spaces and give a new view point to understand aggregation spaces and decision matrices. [ABSTRACT FROM AUTHOR]

Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, (cds) and context directed reversal, (cdr). These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates. This paper investigates mathematical aspects of these two sorting operations. The main result of this paper is a generalization of previously discovered characterizations of cds-sortability of a permutation. The combinatorial structure underlying this generalization suggests natural combinatorial two-player games. These games are the main mathematical innovation of this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with new results for the circular Eisenstein series as well as with a novel approach to Hilbert-Eisenstein series , introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer-Flocke-Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers. [ABSTRACT FROM AUTHOR]